Lecture 33: Direct integration versus modal superposition for a damped system | Multi-Degree of Freedom Dynamics, Modal Analysis and Seismic Response Simulation in Python | EngineeringSkills.com

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Section 1

Welcome and preliminaries

1. Introduction and course overview

04:24 (Preview)

2. Course prerequisites and do I need to know Python?

03:55 (Preview)

3. Getting your coding environment set up

12:04 (Preview)

Section 2

Introduction to ground motion modelling

4. Section 2 overview

03:53 (Preview)

5. Overview of earthquake ground motion 📂

6. Capturing the influence of ground motion 📂

7. Motion transmissibility and isolation 📂

8. Simulating ground motion response 📂

9. Realistic ground motion response 📂

10. Integrating ground acceleration

11. Introduction to response spectra 📂

Section 3

Modelling Multi-DoF Dynamic Systems

12. Section 3 overview

02:00 (Preview)

13. Introduction to MDoF systems

14. MDoF Equations of Motion

15. Direct integration of the coupled EoM

16. Solving the coupled EoM by direct integration 📂

17. Using SciPy’s ODEINT solver

Section 4

Modal Analysis and Decoupling the Equations of Motion

18. Section 4 overview

03:06 (Preview)

19. What is modal analysis and how does it help us?

20. Finding natural frequencies and mode shapes 📂

21. Matrix representation and the eigenproblem 📂

22. Modal matrix and mass normalisation 📂

23. Orthogonality and Decoupling Equations of Motion

24. Modal superposition - forced vibration 📂

25. Comparing modal superposition with direct integration - forced response

26. Visualising the forced vibration response

27. Modal superposition - free vibration 📂

28. Compare modal superposition with direct integration - free vibration

Section 5

Damping Orthogonality

29. Section 5 overview

03:02 (Preview)

30. Rayleigh damping

31. General determination of the damping matrix

32. Calculating the damping matrix 📂

33. Direct integration versus modal superposition for a damped system 📂

Section 6

Bringin it all together: N-storey response to earthquake ground motion

34. Section 6 overview

03:01 (Preview)

35. Equations of motion N-storey shear building 📂

36. Automating modal analysis for NDoF

37. Ground motion response using modal superposition

38. Base shear and overturning moments

39. Visualising the structural response for NDoF

40. Course wrap up and completion certificate

33. Direct integration versus modal superposition for a damped system

Damping Orthogonality

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Multi-Degree of Freedom Dynamics, Modal Analysis and Seismic Response Simulation in Python

Build the knowledge and tools to decode the dynamic response of real-world structures to real-world loads.

After completing this course...

You will be able to model the influence of earthquake-induced ground motion.
You will develop numerical tools to solve the coupled equations of motion for multi-degree of freedom systems.
You will understand the role of modal decomposition in uncoupling the equations of motion and identifying the underlying dynamic characteristics of MDoF systems.

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34. Section 6 overview